Abstract
It is shown that an electron-hole liquid under suitable conditions can become superconducting. This conclusion is reached by using an effective electron-electron interaction which includes vertex corrections and multiple electron-hole scattering by means of local-field corrections. A simple parametrization is proposed for the latter, and the parameters are determined in a self-consistent manner. The superconducting transition temperature ${T}_{c}$, the interaction parameters \ensuremath{\lambda} and \ensuremath{\mu}, and the characteristic frequency ${\ensuremath{\omega}}_{0}$ are studied as functions of density, hole- to electron-mass ratio and valley degeneracy. ${T}_{c}$ is estimated to be of an observable magnitude (${T}_{c}$\ensuremath{\sim}1 K) in some cases of interest. The mechanism of superconductivity is purely based on Coulomb interactions. The intermediate bosons responsible for pairing of the electrons are not acoustic plasmons but correlated pair excitations from the Fermi sea of the holes.
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